The systems of linear equations have the following results: Case 13: No solution, Case 14: Infinite solutions, Case 15: Infinite solutions, Case 16: No solution.
How to solve a system of linear equations by substitution
In this question we must find the solutions to four systems of linear equations by substitution methods, that is, reducing the number of equations to one by substituting variables and simplifying resulting expressions. Now we proceed to solve for each case:
Case 13: Substitute y in the second equation and simplify:
- 2 · x + 2 · x + 7 = - 3
7 = - 3 (The system of linear equations has no solution)
Case 14: Substitute y in the first equation and simplify:
- 10 · x + 2 · (5 · x - 8) = - 16
- 10 · x + 10 · x - 16 = - 16
- 16 = - 16 (The system has an infinite set of solutions)
Case 15: Substitute x in the first equation and simplify:
4 · y - 2 · (2 · y + 8) = - 16
4 · y - 4 · y - 16 = - 16
- 16 = - 16 (The system has an infinite set of solutions)
Case 16: Substitute y in the second equation and simplify:
3 · (- x - 3) = - 3 · x + 15
- 3 · x - 9 = - 3 · x + 15
- 9 = 15 (The system of linear equations has no solution)